Density-Difference Estimation
Abstract
We address the problem of estimating the difference between two probability densities. A naive approach is a two-step procedure of first estimating two densities separately and then computing their difference. However, such a two-step procedure does not necessarily work well because the first step is performed without regard to the second step and thus a small error incurred in the first stage can cause a big error in the second stage. In this paper, we propose a single-shot procedure for directly estimating the density difference without separately estimating two densities. We derive a non-parametric finite-sample error bound for the proposed single-shot density-difference estimator and show that it achieves the optimal convergence rate. The usefulness of the proposed method is also demonstrated experimentally.
Keywords
Cite
@article{arxiv.1207.0099,
title = {Density-Difference Estimation},
author = {Masashi Sugiyama and Takafumi Kanamori and Taiji Suzuki and Marthinus Christoffel du Plessis and Song Liu and Ichiro Takeuchi},
journal= {arXiv preprint arXiv:1207.0099},
year = {2012}
}